In this section, we define the cryptographic primitive used by Mahadev [1]} to obtain a (non-succinct) delegation scheme for \(\textbf {QMA}\)  with classical verification. The primitive is closely related to Regev encryption [2]} and LWE-based “lossy” trapdoor functions [3]}, [4]}, [5]}, but makes use of special-purpose structure relevant for quantum functionality. Most of this special-purpose structure, in particular, the “adaptive hardcore bit”, was introduced in the work of Brakerski, Christiano, Mahadev, Vazirani and Vidick [6]}, but [1]} further requires “dual-mode key generation” in addition to the [6]} properties. Given the numerous special-purpose requirements, we refer to the primitive as “Mahadev randomized trapdoor claw-free functions (rTCFs).”Actually, [1]} requires an extra (second) hardcore bit property (Property 2 of Definition 4.4 in [1]}) that we drop from our definition, as our proof does not require it.
